##############ECHO OF PROBLEM################# ##############temp/mtest8postode.ode################# diff ( y2 , x , 4 ) = y1 - 1.0 ; diff ( y1 , x , 1 ) = m1 * diff ( y2 , x , 3 ) ; ! /* BEGIN FIRST INPUT BLOCK */ Digits=32; max_terms=30; ! /* END FIRST INPUT BLOCK */ /* BEGIN SECOND INPUT BLOCK */ x_start=0.1; x_end=1.4; array_y1_init[0 + 1] = exact_soln_y1(x_start); array_y2_init[0 + 1] = exact_soln_y2(x_start); array_y2_init[1 + 1] = exact_soln_y2p(x_start); array_y2_init[2 + 1] = exact_soln_y2pp(x_start); array_y2_init[3 + 1] = exact_soln_y2ppp(x_start); glob_look_poles=true; glob_max_iter=20; /* END SECOND INPUT BLOCK */ /* BEGIN OVERRIDE BLOCK */ glob_desired_digits_correct=10; glob_display_interval=0.01; glob_look_poles=true; glob_max_iter=1000000000; glob_max_minutes=10.0; glob_subiter_method=3; /* END OVERRIDE BLOCK */ ! /* BEGIN USER DEF BLOCK */ double exact_soln_y1 (double x) { return(1.0 + sin(x)); } double exact_soln_y2 (double x) { return(1.0 + sin(x)); } double exact_soln_y2p (double x) { return( cos(x)); } double exact_soln_y2pp (double x) { return( -sin(x)); } double exact_soln_y2ppp (double x) { return( -cos(x)); } /* END USER DEF BLOCK */ #######END OF ECHO OF PROBLEM################# START of Optimize min_size = 0 min_size = 1 glob_desired_digits_correct = 10 estimated_h = 1e-06 estimated_answer = 1 desired_abs_gbl_error = 1e-10 range = 1.3 estimated_steps = 1300000 step_error = 7.692307692307694e-17 est_needed_step_err = 7.692307692307694e-17 opt_iter = 1 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 2.475466125514875e-184 estimated_step_error = 2.475466125514875e-184 best_h = 2e-06 opt_iter = 2 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.66125750215186e-176 estimated_step_error = 1.66125750215186e-176 best_h = 4e-06 opt_iter = 3 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.114851449339251e-168 estimated_step_error = 1.114851449339251e-168 best_h = 8e-06 opt_iter = 4 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 7.481646952858087e-161 estimated_step_error = 7.481646952858087e-161 best_h = 1.6e-05 opt_iter = 5 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 5.020855692025619e-153 estimated_step_error = 5.020855692025619e-153 best_h = 3.2e-05 opt_iter = 6 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 3.369449168191338e-145 estimated_step_error = 3.369449168191338e-145 best_h = 6.4e-05 opt_iter = 7 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 2.261212414754447e-137 estimated_step_error = 2.261212414754447e-137 best_h = 0.000128 opt_iter = 8 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.517491888843964e-129 estimated_step_error = 1.517491888843964e-129 best_h = 0.000256 opt_iter = 9 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.018395625987249e-121 estimated_step_error = 1.018395625987249e-121 best_h = 0.000512 opt_iter = 10 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 6.834660258501093e-114 estimated_step_error = 6.834660258501093e-114 best_h = 0.001024 opt_iter = 11 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 4.587096249794805e-106 estimated_step_error = 4.587096249794805e-106 best_h = 0.002048 opt_iter = 12 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 3.078929872793795e-98 estimated_step_error = 3.078929872793795e-98 best_h = 0.004096 opt_iter = 13 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 2.067015590707986e-90 estimated_step_error = 2.067015590707986e-90 best_h = 0.008192 opt_iter = 14 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 1.388198559318253e-82 estimated_step_error = 1.388198559318253e-82 best_h = 0.016384 opt_iter = 15 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 9.33010720852238e-75 estimated_step_error = 9.33010720852238e-75 best_h = 0.032768 opt_iter = 16 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 6.280205843940557e-67 estimated_step_error = 6.280205843940557e-67 best_h = 0.065536 opt_iter = 17 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 4.239910926664728e-59 estimated_step_error = 4.239910926664728e-59 best_h = 0.131072 opt_iter = 18 hn_div_ho = 0.5 hn_div_ho_2 = 0.25 hn_div_ho_3 = 0.125 max_estimated_step_error = 2.879361632773575e-51 estimated_step_error = 2.879361632773575e-51 best_h = 0.1 START of Soultion TOP MAIN SOLVE Loop x[1] = 0.1 y2[1] (analytic) = 1.099833416646828 y2[1] (numeric) = 1.099833416646828 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 1.099833416646828 y1[1] (numeric) = 1.099833416646828 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.09933 Order of pole (three term test) = 22.99 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.09933 Order of pole (three term test) = 22.99 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.11 y2[1] (analytic) = 1.109778300837175 y2[1] (numeric) = 1.109778300837175 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 1.109778300837175 y1[1] (numeric) = 1.109778300837175 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1091 Order of pole (three term test) = 22.99 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.1091 Order of pole (three term test) = 22.99 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.12 y2[1] (analytic) = 1.119712207288919 y2[1] (numeric) = 1.119712207288919 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 1.119712207288919 y1[1] (numeric) = 1.119712207288919 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1189 Order of pole (three term test) = 22.99 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.1189 Order of pole (three term test) = 22.99 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.13 y2[1] (analytic) = 1.129634142619695 y2[1] (numeric) = 1.129634142619695 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 1.129634142619695 y1[1] (numeric) = 1.129634142619695 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1285 Order of pole (three term test) = 22.98 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.1285 Order of pole (three term test) = 22.98 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.14 y2[1] (analytic) = 1.139543114644237 y2[1] (numeric) = 1.139543114644237 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 1.139543114644237 y1[1] (numeric) = 1.139543114644237 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1382 Order of pole (three term test) = 22.98 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.1382 Order of pole (three term test) = 22.98 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.15 y2[1] (analytic) = 1.149438132473599 y2[1] (numeric) = 1.149438132473599 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 1.149438132473599 y1[1] (numeric) = 1.149438132473599 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1478 Order of pole (three term test) = 22.98 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.1478 Order of pole (three term test) = 22.98 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.16 y2[1] (analytic) = 1.159318206614246 y2[1] (numeric) = 1.159318206614246 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 1.159318206614246 y1[1] (numeric) = 1.159318206614246 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1573 Order of pole (three term test) = 22.97 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.1573 Order of pole (three term test) = 22.97 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.17 y2[1] (analytic) = 1.169182349066996 y2[1] (numeric) = 1.169182349066996 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 1.169182349066996 y1[1] (numeric) = 1.169182349066996 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1667 Order of pole (three term test) = 22.97 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.1667 Order of pole (three term test) = 22.97 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.18 y2[1] (analytic) = 1.179029573425824 y2[1] (numeric) = 1.179029573425824 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 1.179029573425824 y1[1] (numeric) = 1.179029573425824 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1761 Order of pole (three term test) = 22.97 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.1761 Order of pole (three term test) = 22.97 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.1900000000000001 y2[1] (analytic) = 1.188858894976501 y2[1] (numeric) = 1.188858894976501 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 1.188858894976501 y1[1] (numeric) = 1.188858894976501 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1855 Order of pole (three term test) = 22.96 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.1855 Order of pole (three term test) = 22.96 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.2000000000000001 y2[1] (analytic) = 1.198669330795061 y2[1] (numeric) = 1.198669330795061 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 1.198669330795061 y1[1] (numeric) = 1.198669330795061 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1947 Order of pole (three term test) = 22.96 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.1947 Order of pole (three term test) = 22.96 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.2100000000000001 y2[1] (analytic) = 1.2084598998461 y2[1] (numeric) = 1.2084598998461 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 1.2084598998461 y1[1] (numeric) = 1.2084598998461 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2039 Order of pole (three term test) = 22.96 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2039 Order of pole (three term test) = 22.96 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.2200000000000001 y2[1] (analytic) = 1.218229623080869 y2[1] (numeric) = 1.218229623080869 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 1.218229623080869 y1[1] (numeric) = 1.218229623080869 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.213 Order of pole (three term test) = 22.95 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.213 Order of pole (three term test) = 22.95 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.2300000000000001 y2[1] (analytic) = 1.227977523535188 y2[1] (numeric) = 1.227977523535188 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 1.227977523535188 y1[1] (numeric) = 1.227977523535188 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.222 Order of pole (three term test) = 22.95 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.222 Order of pole (three term test) = 22.95 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.2400000000000001 y2[1] (analytic) = 1.237702626427135 y2[1] (numeric) = 1.237702626427135 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 1.237702626427135 y1[1] (numeric) = 1.237702626427135 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2309 Order of pole (three term test) = 22.94 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2309 Order of pole (three term test) = 22.94 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.2500000000000001 y2[1] (analytic) = 1.247403959254523 y2[1] (numeric) = 1.247403959254523 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 1.247403959254523 y1[1] (numeric) = 1.247403959254523 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2397 Order of pole (three term test) = 22.94 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2397 Order of pole (three term test) = 22.94 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.2600000000000001 y2[1] (analytic) = 1.257080551892155 y2[1] (numeric) = 1.257080551892155 absolute error = 2.220446049250313e-16 relative error = 1.766351444947662e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 1.257080551892155 y1[1] (numeric) = 1.257080551892155 absolute error = 2.220446049250313e-16 relative error = 1.766351444947662e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2484 Order of pole (three term test) = 22.93 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2484 Order of pole (three term test) = 22.93 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.2700000000000001 y2[1] (analytic) = 1.266731436688831 y2[1] (numeric) = 1.266731436688831 absolute error = 2.220446049250313e-16 relative error = 1.75289409020624e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 1.266731436688831 y1[1] (numeric) = 1.266731436688831 absolute error = 2.220446049250313e-16 relative error = 1.75289409020624e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2571 Order of pole (three term test) = 22.93 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2571 Order of pole (three term test) = 22.93 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.2800000000000001 y2[1] (analytic) = 1.276355648564114 y2[1] (numeric) = 1.276355648564114 absolute error = 2.220446049250313e-16 relative error = 1.739676595428782e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 1.276355648564114 y1[1] (numeric) = 1.276355648564114 absolute error = 2.220446049250313e-16 relative error = 1.739676595428782e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2656 Order of pole (three term test) = 22.92 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2656 Order of pole (three term test) = 22.92 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.2900000000000001 y2[1] (analytic) = 1.285952225104836 y2[1] (numeric) = 1.285952225104835 absolute error = 2.220446049250313e-16 relative error = 1.726694045005672e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 1.285952225104836 y1[1] (numeric) = 1.285952225104835 absolute error = 2.220446049250313e-16 relative error = 1.726694045005672e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.274 Order of pole (three term test) = 22.92 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.274 Order of pole (three term test) = 22.92 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.3000000000000002 y2[1] (analytic) = 1.29552020666134 y2[1] (numeric) = 1.295520206661339 absolute error = 4.440892098500626e-16 relative error = 3.427883313333386e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 1.29552020666134 y1[1] (numeric) = 1.295520206661339 absolute error = 4.440892098500626e-16 relative error = 3.427883313333386e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2823 Order of pole (three term test) = 22.91 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2823 Order of pole (three term test) = 22.91 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.3100000000000002 y2[1] (analytic) = 1.305058636443444 y2[1] (numeric) = 1.305058636443443 absolute error = 2.220446049250313e-16 relative error = 1.701414777271227e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 1.305058636443444 y1[1] (numeric) = 1.305058636443443 absolute error = 2.220446049250313e-16 relative error = 1.701414777271227e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2905 Order of pole (three term test) = 22.91 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2905 Order of pole (three term test) = 22.91 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.3200000000000002 y2[1] (analytic) = 1.314566560616118 y2[1] (numeric) = 1.314566560616118 absolute error = 2.220446049250313e-16 relative error = 1.689108878754396e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 1.314566560616118 y1[1] (numeric) = 1.314566560616118 absolute error = 2.220446049250313e-16 relative error = 1.689108878754396e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2986 Order of pole (three term test) = 22.9 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2986 Order of pole (three term test) = 22.9 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.3300000000000002 y2[1] (analytic) = 1.324043028394869 y2[1] (numeric) = 1.324043028394868 absolute error = 2.220446049250313e-16 relative error = 1.677019554222607e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 1.324043028394869 y1[1] (numeric) = 1.324043028394868 absolute error = 2.220446049250313e-16 relative error = 1.677019554222607e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3066 Order of pole (three term test) = 22.89 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3066 Order of pole (three term test) = 22.89 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.3400000000000002 y2[1] (analytic) = 1.333487092140815 y2[1] (numeric) = 1.333487092140814 absolute error = 2.220446049250313e-16 relative error = 1.665142514192283e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 1.333487092140815 y1[1] (numeric) = 1.333487092140814 absolute error = 2.220446049250313e-16 relative error = 1.665142514192283e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3144 Order of pole (three term test) = 22.89 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3144 Order of pole (three term test) = 22.89 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.3500000000000002 y2[1] (analytic) = 1.342897807455452 y2[1] (numeric) = 1.342897807455451 absolute error = 2.220446049250313e-16 relative error = 1.653473582965823e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 1.342897807455452 y1[1] (numeric) = 1.342897807455451 absolute error = 2.220446049250313e-16 relative error = 1.653473582965823e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3221 Order of pole (three term test) = 22.88 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3221 Order of pole (three term test) = 22.88 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.3600000000000002 y2[1] (analytic) = 1.35227423327509 y2[1] (numeric) = 1.35227423327509 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 1.35227423327509 y1[1] (numeric) = 1.35227423327509 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3297 Order of pole (three term test) = 22.88 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3297 Order of pole (three term test) = 22.88 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.3700000000000002 y2[1] (analytic) = 1.361615431964962 y2[1] (numeric) = 1.361615431964962 absolute error = 2.220446049250313e-16 relative error = 1.630743892235389e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 1.361615431964962 y1[1] (numeric) = 1.361615431964962 absolute error = 2.220446049250313e-16 relative error = 1.630743892235389e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3371 Order of pole (three term test) = 22.87 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3371 Order of pole (three term test) = 22.87 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.3800000000000002 y2[1] (analytic) = 1.370920469412983 y2[1] (numeric) = 1.370920469412983 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 1.370920469412983 y1[1] (numeric) = 1.370920469412983 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3445 Order of pole (three term test) = 22.86 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3445 Order of pole (three term test) = 22.86 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.3900000000000002 y2[1] (analytic) = 1.380188415123162 y2[1] (numeric) = 1.380188415123162 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 1.380188415123162 y1[1] (numeric) = 1.380188415123162 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3516 Order of pole (three term test) = 22.86 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3516 Order of pole (three term test) = 22.86 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.4000000000000002 y2[1] (analytic) = 1.389418342308651 y2[1] (numeric) = 1.389418342308651 absolute error = 2.220446049250313e-16 relative error = 1.59811194485948e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 1.389418342308651 y1[1] (numeric) = 1.389418342308651 absolute error = 2.220446049250313e-16 relative error = 1.59811194485948e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3587 Order of pole (three term test) = 22.85 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3587 Order of pole (three term test) = 22.85 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.4100000000000003 y2[1] (analytic) = 1.398609327984423 y2[1] (numeric) = 1.398609327984423 absolute error = 2.220446049250313e-16 relative error = 1.587609924245438e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 1.398609327984423 y1[1] (numeric) = 1.398609327984423 absolute error = 2.220446049250313e-16 relative error = 1.587609924245438e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3656 Order of pole (three term test) = 22.84 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3656 Order of pole (three term test) = 22.84 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.4200000000000003 y2[1] (analytic) = 1.40776045305957 y2[1] (numeric) = 1.40776045305957 absolute error = 2.220446049250313e-16 relative error = 1.57728969046153e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 1.40776045305957 y1[1] (numeric) = 1.40776045305957 absolute error = 2.220446049250313e-16 relative error = 1.57728969046153e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3723 Order of pole (three term test) = 22.83 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3723 Order of pole (three term test) = 22.83 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.4300000000000003 y2[1] (analytic) = 1.416870802429211 y2[1] (numeric) = 1.416870802429211 absolute error = 2.220446049250313e-16 relative error = 1.567147862348056e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 1.416870802429211 y1[1] (numeric) = 1.416870802429211 absolute error = 2.220446049250313e-16 relative error = 1.567147862348056e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3789 Order of pole (three term test) = 22.83 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3789 Order of pole (three term test) = 22.83 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.4400000000000003 y2[1] (analytic) = 1.425939465066 y2[1] (numeric) = 1.425939465066 absolute error = 2.220446049250313e-16 relative error = 1.557181145237143e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 1.425939465066 y1[1] (numeric) = 1.425939465066 absolute error = 2.220446049250313e-16 relative error = 1.557181145237143e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3854 Order of pole (three term test) = 22.82 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3854 Order of pole (three term test) = 22.82 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.4500000000000003 y2[1] (analytic) = 1.43496553411123 y2[1] (numeric) = 1.43496553411123 absolute error = 2.220446049250313e-16 relative error = 1.547386328428845e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 1.43496553411123 y1[1] (numeric) = 1.43496553411123 absolute error = 2.220446049250313e-16 relative error = 1.547386328428845e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3917 Order of pole (three term test) = 22.81 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3917 Order of pole (three term test) = 22.81 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.4600000000000003 y2[1] (analytic) = 1.44394810696552 y2[1] (numeric) = 1.44394810696552 absolute error = 2.220446049250313e-16 relative error = 1.537760282754632e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 1.44394810696552 y1[1] (numeric) = 1.44394810696552 absolute error = 2.220446049250313e-16 relative error = 1.537760282754632e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3978 Order of pole (three term test) = 22.8 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3978 Order of pole (three term test) = 22.8 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.4700000000000003 y2[1] (analytic) = 1.452886285379068 y2[1] (numeric) = 1.452886285379068 absolute error = 2.220446049250313e-16 relative error = 1.528299958224867e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 1.452886285379068 y1[1] (numeric) = 1.452886285379068 absolute error = 2.220446049250313e-16 relative error = 1.528299958224867e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4038 Order of pole (three term test) = 22.79 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4038 Order of pole (three term test) = 22.79 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.4800000000000003 y2[1] (analytic) = 1.461779175541483 y2[1] (numeric) = 1.461779175541483 absolute error = 2.220446049250313e-16 relative error = 1.519002381757011e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 1.461779175541483 y1[1] (numeric) = 1.461779175541483 absolute error = 2.220446049250313e-16 relative error = 1.519002381757011e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4096 Order of pole (three term test) = 22.79 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4096 Order of pole (three term test) = 22.79 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.4900000000000003 y2[1] (analytic) = 1.470625888171158 y2[1] (numeric) = 1.470625888171158 absolute error = 2.220446049250313e-16 relative error = 1.509864654981435e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 1.470625888171158 y1[1] (numeric) = 1.470625888171158 absolute error = 2.220446049250313e-16 relative error = 1.509864654981435e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4152 Order of pole (three term test) = 22.78 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4152 Order of pole (three term test) = 22.78 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.5000000000000003 y2[1] (analytic) = 1.479425538604203 y2[1] (numeric) = 1.479425538604203 absolute error = 2.220446049250313e-16 relative error = 1.500883952121877e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 1.479425538604203 y1[1] (numeric) = 1.479425538604203 absolute error = 2.220446049250313e-16 relative error = 1.500883952121877e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4207 Order of pole (three term test) = 22.77 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4207 Order of pole (three term test) = 22.77 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.5100000000000003 y2[1] (analytic) = 1.488177246882908 y2[1] (numeric) = 1.488177246882908 absolute error = 2.220446049250313e-16 relative error = 1.492057517947673e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 1.488177246882908 y1[1] (numeric) = 1.488177246882908 absolute error = 2.220446049250313e-16 relative error = 1.492057517947673e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4261 Order of pole (three term test) = 22.76 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4261 Order of pole (three term test) = 22.76 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.5200000000000004 y2[1] (analytic) = 1.496880137843737 y2[1] (numeric) = 1.496880137843737 absolute error = 2.220446049250313e-16 relative error = 1.483382665795056e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 1.496880137843737 y1[1] (numeric) = 1.496880137843737 absolute error = 2.220446049250313e-16 relative error = 1.483382665795056e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4312 Order of pole (three term test) = 22.75 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4312 Order of pole (three term test) = 22.75 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.5300000000000004 y2[1] (analytic) = 1.505533341204847 y2[1] (numeric) = 1.505533341204847 absolute error = 2.220446049250313e-16 relative error = 1.474856775654889e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 1.505533341204847 y1[1] (numeric) = 1.505533341204847 absolute error = 2.220446049250313e-16 relative error = 1.474856775654889e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4362 Order of pole (three term test) = 22.74 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4362 Order of pole (three term test) = 22.74 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.5400000000000004 y2[1] (analytic) = 1.514135991653113 y2[1] (numeric) = 1.514135991653113 absolute error = 2.220446049250313e-16 relative error = 1.466477292324357e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 1.514135991653113 y1[1] (numeric) = 1.514135991653113 absolute error = 2.220446049250313e-16 relative error = 1.466477292324357e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.441 Order of pole (three term test) = 22.74 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.441 Order of pole (three term test) = 22.74 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.5500000000000004 y2[1] (analytic) = 1.522687228930659 y2[1] (numeric) = 1.522687228930659 absolute error = 2.220446049250313e-16 relative error = 1.458241723620201e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 1.522687228930659 y1[1] (numeric) = 1.522687228930659 absolute error = 2.220446049250313e-16 relative error = 1.458241723620201e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4456 Order of pole (three term test) = 22.73 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4456 Order of pole (three term test) = 22.73 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.5600000000000004 y2[1] (analytic) = 1.531186197920884 y2[1] (numeric) = 1.531186197920883 absolute error = 2.220446049250313e-16 relative error = 1.450147638651223e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 1.531186197920884 y1[1] (numeric) = 1.531186197920883 absolute error = 2.220446049250313e-16 relative error = 1.450147638651223e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4501 Order of pole (three term test) = 22.72 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4501 Order of pole (three term test) = 22.72 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.5700000000000004 y2[1] (analytic) = 1.539632048733969 y2[1] (numeric) = 1.539632048733969 absolute error = 2.220446049250313e-16 relative error = 1.442192666147845e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 1.539632048733969 y1[1] (numeric) = 1.539632048733969 absolute error = 2.220446049250313e-16 relative error = 1.442192666147845e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4543 Order of pole (three term test) = 22.71 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4543 Order of pole (three term test) = 22.71 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.5800000000000004 y2[1] (analytic) = 1.548023936791874 y2[1] (numeric) = 1.548023936791874 absolute error = 4.440892098500626e-16 relative error = 2.868748985693292e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 1.548023936791874 y1[1] (numeric) = 1.548023936791874 absolute error = 4.440892098500626e-16 relative error = 2.868748985693292e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4584 Order of pole (three term test) = 22.7 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4584 Order of pole (three term test) = 22.7 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.5900000000000004 y2[1] (analytic) = 1.556361022912784 y2[1] (numeric) = 1.556361022912784 absolute error = 2.220446049250313e-16 relative error = 1.426690861927826e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 1.556361022912784 y1[1] (numeric) = 1.556361022912784 absolute error = 2.220446049250313e-16 relative error = 1.426690861927826e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4623 Order of pole (three term test) = 22.69 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4623 Order of pole (three term test) = 22.69 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.6000000000000004 y2[1] (analytic) = 1.564642473395036 y2[1] (numeric) = 1.564642473395035 absolute error = 4.440892098500626e-16 relative error = 2.838279143007391e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 1.564642473395036 y1[1] (numeric) = 1.564642473395035 absolute error = 4.440892098500626e-16 relative error = 2.838279143007391e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.466 Order of pole (three term test) = 22.68 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.466 Order of pole (three term test) = 22.68 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.6100000000000004 y2[1] (analytic) = 1.572867460100482 y2[1] (numeric) = 1.572867460100481 absolute error = 6.661338147750939e-16 relative error = 4.235155419468964e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 1.572867460100482 y1[1] (numeric) = 1.572867460100481 absolute error = 6.661338147750939e-16 relative error = 4.235155419468964e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4695 Order of pole (three term test) = 22.67 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4695 Order of pole (three term test) = 22.67 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.6200000000000004 y2[1] (analytic) = 1.581035160537305 y2[1] (numeric) = 1.581035160537305 absolute error = 4.440892098500626e-16 relative error = 2.808850941045116e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 1.581035160537305 y1[1] (numeric) = 1.581035160537305 absolute error = 4.440892098500626e-16 relative error = 2.808850941045116e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4729 Order of pole (three term test) = 22.66 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4729 Order of pole (three term test) = 22.66 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.6300000000000004 y2[1] (analytic) = 1.58914475794227 y2[1] (numeric) = 1.58914475794227 absolute error = 4.440892098500626e-16 relative error = 2.794517035849514e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 1.58914475794227 y1[1] (numeric) = 1.58914475794227 absolute error = 4.440892098500626e-16 relative error = 2.794517035849514e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.476 Order of pole (three term test) = 22.65 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.476 Order of pole (three term test) = 22.65 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.6400000000000005 y2[1] (analytic) = 1.597195441362393 y2[1] (numeric) = 1.597195441362392 absolute error = 4.440892098500626e-16 relative error = 2.780431238091055e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 1.597195441362393 y1[1] (numeric) = 1.597195441362392 absolute error = 4.440892098500626e-16 relative error = 2.780431238091055e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.479 Order of pole (three term test) = 22.64 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.479 Order of pole (three term test) = 22.64 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.6500000000000005 y2[1] (analytic) = 1.60518640573604 y2[1] (numeric) = 1.60518640573604 absolute error = 2.220446049250313e-16 relative error = 1.383294825644971e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 1.60518640573604 y1[1] (numeric) = 1.60518640573604 absolute error = 2.220446049250313e-16 relative error = 1.383294825644971e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4818 Order of pole (three term test) = 22.63 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4818 Order of pole (three term test) = 22.63 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.6600000000000005 y2[1] (analytic) = 1.613116851973434 y2[1] (numeric) = 1.613116851973434 absolute error = 4.440892098500626e-16 relative error = 2.752988472637791e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 1.613116851973434 y1[1] (numeric) = 1.613116851973434 absolute error = 4.440892098500626e-16 relative error = 2.752988472637791e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4844 Order of pole (three term test) = 22.62 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4844 Order of pole (three term test) = 22.62 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.6700000000000005 y2[1] (analytic) = 1.62098598703656 y2[1] (numeric) = 1.62098598703656 absolute error = 4.440892098500626e-16 relative error = 2.739623990593119e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 1.62098598703656 y1[1] (numeric) = 1.62098598703656 absolute error = 4.440892098500626e-16 relative error = 2.739623990593119e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4867 Order of pole (three term test) = 22.61 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4867 Order of pole (three term test) = 22.61 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.6800000000000005 y2[1] (analytic) = 1.628793024018469 y2[1] (numeric) = 1.628793024018468 absolute error = 4.440892098500626e-16 relative error = 2.726492582553123e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 1.628793024018469 y1[1] (numeric) = 1.628793024018468 absolute error = 4.440892098500626e-16 relative error = 2.726492582553123e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4889 Order of pole (three term test) = 22.6 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4889 Order of pole (three term test) = 22.6 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.6900000000000005 y2[1] (analytic) = 1.636537182221968 y2[1] (numeric) = 1.636537182221968 absolute error = 4.440892098500626e-16 relative error = 2.713590712599095e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 1.636537182221968 y1[1] (numeric) = 1.636537182221968 absolute error = 4.440892098500626e-16 relative error = 2.713590712599095e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4909 Order of pole (three term test) = 22.59 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4909 Order of pole (three term test) = 22.59 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.7000000000000005 y2[1] (analytic) = 1.644217687237691 y2[1] (numeric) = 1.644217687237691 absolute error = 4.440892098500626e-16 relative error = 2.70091492931291e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 1.644217687237691 y1[1] (numeric) = 1.644217687237691 absolute error = 4.440892098500626e-16 relative error = 2.70091492931291e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4927 Order of pole (three term test) = 22.58 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4927 Order of pole (three term test) = 22.58 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.7100000000000005 y2[1] (analytic) = 1.651833771021537 y2[1] (numeric) = 1.651833771021537 absolute error = 4.440892098500626e-16 relative error = 2.688461863662142e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 1.651833771021537 y1[1] (numeric) = 1.651833771021537 absolute error = 4.440892098500626e-16 relative error = 2.688461863662142e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4943 Order of pole (three term test) = 22.58 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4943 Order of pole (three term test) = 22.58 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.7200000000000005 y2[1] (analytic) = 1.659384671971474 y2[1] (numeric) = 1.659384671971473 absolute error = 4.440892098500626e-16 relative error = 2.676228226951448e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 1.659384671971474 y1[1] (numeric) = 1.659384671971473 absolute error = 4.440892098500626e-16 relative error = 2.676228226951448e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4957 Order of pole (three term test) = 22.57 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4957 Order of pole (three term test) = 22.57 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.7300000000000005 y2[1] (analytic) = 1.666869635003698 y2[1] (numeric) = 1.666869635003698 absolute error = 4.440892098500626e-16 relative error = 2.664210808837953e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 1.666869635003698 y1[1] (numeric) = 1.666869635003698 absolute error = 4.440892098500626e-16 relative error = 2.664210808837953e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4969 Order of pole (three term test) = 22.56 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4969 Order of pole (three term test) = 22.56 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.7400000000000005 y2[1] (analytic) = 1.674287911628145 y2[1] (numeric) = 1.674287911628145 absolute error = 4.440892098500626e-16 relative error = 2.652406475408475e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 1.674287911628145 y1[1] (numeric) = 1.674287911628145 absolute error = 4.440892098500626e-16 relative error = 2.652406475408475e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4979 Order of pole (three term test) = 22.55 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4979 Order of pole (three term test) = 22.55 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.7500000000000006 y2[1] (analytic) = 1.681638760023334 y2[1] (numeric) = 1.681638760023334 absolute error = 2.220446049250313e-16 relative error = 1.320406083658242e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 1.681638760023334 y1[1] (numeric) = 1.681638760023334 absolute error = 2.220446049250313e-16 relative error = 1.320406083658242e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4987 Order of pole (three term test) = 22.54 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4987 Order of pole (three term test) = 22.54 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.7600000000000006 y2[1] (analytic) = 1.688921445110552 y2[1] (numeric) = 1.688921445110551 absolute error = 2.220446049250313e-16 relative error = 1.314712448988395e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 1.688921445110552 y1[1] (numeric) = 1.688921445110551 absolute error = 2.220446049250313e-16 relative error = 1.314712448988395e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4994 Order of pole (three term test) = 22.53 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4994 Order of pole (three term test) = 22.53 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.7700000000000006 y2[1] (analytic) = 1.696135238627357 y2[1] (numeric) = 1.696135238627357 absolute error = 2.220446049250313e-16 relative error = 1.309120875908025e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 1.696135238627357 y1[1] (numeric) = 1.696135238627357 absolute error = 2.220446049250313e-16 relative error = 1.309120875908025e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4998 Order of pole (three term test) = 22.52 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4998 Order of pole (three term test) = 22.52 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.7800000000000006 y2[1] (analytic) = 1.703279419200411 y2[1] (numeric) = 1.70327941920041 absolute error = 2.220446049250313e-16 relative error = 1.303629941288601e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 1.703279419200411 y1[1] (numeric) = 1.70327941920041 absolute error = 2.220446049250313e-16 relative error = 1.303629941288601e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.5 Order of pole (three term test) = 22.51 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.5 Order of pole (three term test) = 22.51 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.7900000000000006 y2[1] (analytic) = 1.710353272417608 y2[1] (numeric) = 1.710353272417608 absolute error = 2.220446049250313e-16 relative error = 1.298238255838036e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 1.710353272417608 y1[1] (numeric) = 1.710353272417608 absolute error = 2.220446049250313e-16 relative error = 1.298238255838036e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.5 Order of pole (three term test) = 22.5 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.5 Order of pole (three term test) = 22.5 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.8000000000000006 y2[1] (analytic) = 1.717356090899523 y2[1] (numeric) = 1.717356090899523 absolute error = 2.220446049250313e-16 relative error = 1.292944463304218e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 1.717356090899523 y1[1] (numeric) = 1.717356090899523 absolute error = 2.220446049250313e-16 relative error = 1.292944463304218e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4998 Order of pole (three term test) = 22.49 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4998 Order of pole (three term test) = 22.49 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.8100000000000006 y2[1] (analytic) = 1.724287174370143 y2[1] (numeric) = 1.724287174370143 absolute error = 2.220446049250313e-16 relative error = 1.287747239702928e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 1.724287174370143 y1[1] (numeric) = 1.724287174370143 absolute error = 2.220446049250313e-16 relative error = 1.287747239702928e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4994 Order of pole (three term test) = 22.48 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4994 Order of pole (three term test) = 22.48 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.8200000000000006 y2[1] (analytic) = 1.731145829726896 y2[1] (numeric) = 1.731145829726896 absolute error = 2.220446049250313e-16 relative error = 1.282645292569378e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 1.731145829726896 y1[1] (numeric) = 1.731145829726896 absolute error = 2.220446049250313e-16 relative error = 1.282645292569378e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4988 Order of pole (three term test) = 22.47 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4988 Order of pole (three term test) = 22.47 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.8300000000000006 y2[1] (analytic) = 1.737931371109963 y2[1] (numeric) = 1.737931371109963 absolute error = 2.220446049250313e-16 relative error = 1.277637360232575e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 1.737931371109963 y1[1] (numeric) = 1.737931371109963 absolute error = 2.220446049250313e-16 relative error = 1.277637360232575e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.498 Order of pole (three term test) = 22.46 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.498 Order of pole (three term test) = 22.46 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.8400000000000006 y2[1] (analytic) = 1.74464311997086 y2[1] (numeric) = 1.744643119970859 absolute error = 4.440892098500626e-16 relative error = 2.545444422223613e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 1.74464311997086 y1[1] (numeric) = 1.744643119970859 absolute error = 4.440892098500626e-16 relative error = 2.545444422223613e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.497 Order of pole (three term test) = 22.45 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.497 Order of pole (three term test) = 22.45 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.8500000000000006 y2[1] (analytic) = 1.751280405140293 y2[1] (numeric) = 1.751280405140293 absolute error = 4.440892098500626e-16 relative error = 2.53579728606903e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 1.751280405140293 y1[1] (numeric) = 1.751280405140293 absolute error = 4.440892098500626e-16 relative error = 2.53579728606903e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4958 Order of pole (three term test) = 22.44 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4958 Order of pole (three term test) = 22.44 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.8600000000000007 y2[1] (analytic) = 1.757842562895277 y2[1] (numeric) = 1.757842562895277 absolute error = 2.220446049250313e-16 relative error = 1.263165482574901e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 1.757842562895277 y1[1] (numeric) = 1.757842562895277 absolute error = 2.220446049250313e-16 relative error = 1.263165482574901e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4944 Order of pole (three term test) = 22.43 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4944 Order of pole (three term test) = 22.43 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.8700000000000007 y2[1] (analytic) = 1.764328937025506 y2[1] (numeric) = 1.764328937025505 absolute error = 2.220446049250313e-16 relative error = 1.258521584412586e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 1.764328937025506 y1[1] (numeric) = 1.764328937025505 absolute error = 2.220446049250313e-16 relative error = 1.258521584412586e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4929 Order of pole (three term test) = 22.42 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4929 Order of pole (three term test) = 22.42 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.8800000000000007 y2[1] (analytic) = 1.77073887889897 y2[1] (numeric) = 1.77073887889897 absolute error = 2.220446049250313e-16 relative error = 1.253965830710718e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 1.77073887889897 y1[1] (numeric) = 1.77073887889897 absolute error = 2.220446049250313e-16 relative error = 1.253965830710718e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4911 Order of pole (three term test) = 22.41 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4911 Order of pole (three term test) = 22.41 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.8900000000000007 y2[1] (analytic) = 1.777071747526824 y2[1] (numeric) = 1.777071747526824 absolute error = 2.220446049250313e-16 relative error = 1.249497130512901e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 1.777071747526824 y1[1] (numeric) = 1.777071747526824 absolute error = 2.220446049250313e-16 relative error = 1.249497130512901e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4891 Order of pole (three term test) = 22.4 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4891 Order of pole (three term test) = 22.4 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.9000000000000007 y2[1] (analytic) = 1.783326909627484 y2[1] (numeric) = 1.783326909627484 absolute error = 2.220446049250313e-16 relative error = 1.245114419158369e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 1.783326909627484 y1[1] (numeric) = 1.783326909627484 absolute error = 2.220446049250313e-16 relative error = 1.245114419158369e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4869 Order of pole (three term test) = 22.39 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4869 Order of pole (three term test) = 22.39 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.9100000000000007 y2[1] (analytic) = 1.789503739689951 y2[1] (numeric) = 1.78950373968995 absolute error = 4.440892098500626e-16 relative error = 2.481633315429704e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 1.789503739689951 y1[1] (numeric) = 1.78950373968995 absolute error = 4.440892098500626e-16 relative error = 2.481633315429704e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4846 Order of pole (three term test) = 22.38 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4846 Order of pole (three term test) = 22.38 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.9200000000000007 y2[1] (analytic) = 1.795601620036366 y2[1] (numeric) = 1.795601620036366 absolute error = 4.440892098500626e-16 relative error = 2.473205664857155e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 1.795601620036366 y1[1] (numeric) = 1.795601620036366 absolute error = 4.440892098500626e-16 relative error = 2.473205664857155e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.482 Order of pole (three term test) = 22.37 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.482 Order of pole (three term test) = 22.37 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.9300000000000007 y2[1] (analytic) = 1.801619940883778 y2[1] (numeric) = 1.801619940883777 absolute error = 4.440892098500626e-16 relative error = 2.464943908381789e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 1.801619940883778 y1[1] (numeric) = 1.801619940883777 absolute error = 4.440892098500626e-16 relative error = 2.464943908381789e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4792 Order of pole (three term test) = 22.36 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4792 Order of pole (three term test) = 22.36 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.9400000000000007 y2[1] (analytic) = 1.807558100405115 y2[1] (numeric) = 1.807558100405114 absolute error = 4.440892098500626e-16 relative error = 2.456846116042036e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 1.807558100405115 y1[1] (numeric) = 1.807558100405114 absolute error = 4.440892098500626e-16 relative error = 2.456846116042036e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4763 Order of pole (three term test) = 22.35 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4763 Order of pole (three term test) = 22.35 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.9500000000000007 y2[1] (analytic) = 1.813415504789374 y2[1] (numeric) = 1.813415504789374 absolute error = 6.661338147750939e-16 relative error = 3.673365607693227e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 1.813415504789374 y1[1] (numeric) = 1.813415504789374 absolute error = 6.661338147750939e-16 relative error = 3.673365607693227e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4732 Order of pole (three term test) = 22.34 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4732 Order of pole (three term test) = 22.34 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.9600000000000007 y2[1] (analytic) = 1.819191568300999 y2[1] (numeric) = 1.819191568300998 absolute error = 4.440892098500626e-16 relative error = 2.441134939212651e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 1.819191568300999 y1[1] (numeric) = 1.819191568300998 absolute error = 4.440892098500626e-16 relative error = 2.441134939212651e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4698 Order of pole (three term test) = 22.33 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4698 Order of pole (three term test) = 22.33 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.9700000000000008 y2[1] (analytic) = 1.824885713338451 y2[1] (numeric) = 1.82488571333845 absolute error = 6.661338147750939e-16 relative error = 3.650276890800285e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 1.824885713338451 y1[1] (numeric) = 1.82488571333845 absolute error = 6.661338147750939e-16 relative error = 3.650276890800285e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4663 Order of pole (three term test) = 22.32 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4663 Order of pole (three term test) = 22.32 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.9800000000000008 y2[1] (analytic) = 1.830497370491971 y2[1] (numeric) = 1.83049737049197 absolute error = 4.440892098500626e-16 relative error = 2.426057622419352e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 1.830497370491971 y1[1] (numeric) = 1.83049737049197 absolute error = 4.440892098500626e-16 relative error = 2.426057622419352e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4626 Order of pole (three term test) = 22.31 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4626 Order of pole (three term test) = 22.31 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 0.9900000000000008 y2[1] (analytic) = 1.836025978600521 y2[1] (numeric) = 1.836025978600521 absolute error = 2.220446049250313e-16 relative error = 1.209376160866095e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 1.836025978600521 y1[1] (numeric) = 1.836025978600521 absolute error = 2.220446049250313e-16 relative error = 1.209376160866095e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4587 Order of pole (three term test) = 22.3 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4587 Order of pole (three term test) = 22.3 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.000000000000001 y2[1] (analytic) = 1.841470984807897 y2[1] (numeric) = 1.841470984807897 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 1.841470984807897 y1[1] (numeric) = 1.841470984807897 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4546 Order of pole (three term test) = 22.29 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4546 Order of pole (three term test) = 22.29 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.010000000000001 y2[1] (analytic) = 1.846831844618015 y2[1] (numeric) = 1.846831844618015 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 1.846831844618015 y1[1] (numeric) = 1.846831844618015 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4504 Order of pole (three term test) = 22.28 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4504 Order of pole (three term test) = 22.28 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.020000000000001 y2[1] (analytic) = 1.852108021949363 y2[1] (numeric) = 1.852108021949363 absolute error = 2.220446049250313e-16 relative error = 1.198875023991997e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 1.852108021949363 y1[1] (numeric) = 1.852108021949363 absolute error = 2.220446049250313e-16 relative error = 1.198875023991997e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.446 Order of pole (three term test) = 22.27 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.446 Order of pole (three term test) = 22.27 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.030000000000001 y2[1] (analytic) = 1.857298989188604 y2[1] (numeric) = 1.857298989188604 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 1.857298989188604 y1[1] (numeric) = 1.857298989188604 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4414 Order of pole (three term test) = 22.27 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4414 Order of pole (three term test) = 22.27 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.040000000000001 y2[1] (analytic) = 1.862404227243339 y2[1] (numeric) = 1.862404227243339 absolute error = 2.220446049250313e-16 relative error = 1.19224710552603e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 1.862404227243339 y1[1] (numeric) = 1.862404227243339 absolute error = 2.220446049250313e-16 relative error = 1.19224710552603e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4366 Order of pole (three term test) = 22.26 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4366 Order of pole (three term test) = 22.26 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.050000000000001 y2[1] (analytic) = 1.867423225594017 y2[1] (numeric) = 1.867423225594017 absolute error = 2.220446049250313e-16 relative error = 1.189042750897564e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 1.867423225594017 y1[1] (numeric) = 1.867423225594017 absolute error = 2.220446049250313e-16 relative error = 1.189042750897564e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4316 Order of pole (three term test) = 22.25 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4316 Order of pole (three term test) = 22.25 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.060000000000001 y2[1] (analytic) = 1.872355482344987 y2[1] (numeric) = 1.872355482344986 absolute error = 2.220446049250313e-16 relative error = 1.185910512286571e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 1.872355482344987 y1[1] (numeric) = 1.872355482344986 absolute error = 2.220446049250313e-16 relative error = 1.185910512286571e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4265 Order of pole (three term test) = 22.24 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4265 Order of pole (three term test) = 22.24 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.070000000000001 y2[1] (analytic) = 1.877200504274682 y2[1] (numeric) = 1.877200504274682 absolute error = 2.220446049250313e-16 relative error = 1.182849697831429e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 1.877200504274682 y1[1] (numeric) = 1.877200504274682 absolute error = 2.220446049250313e-16 relative error = 1.182849697831429e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4212 Order of pole (three term test) = 22.23 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4212 Order of pole (three term test) = 22.23 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.080000000000001 y2[1] (analytic) = 1.881957806884948 y2[1] (numeric) = 1.881957806884948 absolute error = 2.220446049250313e-16 relative error = 1.179859634008287e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 1.881957806884948 y1[1] (numeric) = 1.881957806884948 absolute error = 2.220446049250313e-16 relative error = 1.179859634008287e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4157 Order of pole (three term test) = 22.22 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4157 Order of pole (three term test) = 22.22 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.090000000000001 y2[1] (analytic) = 1.886626914449488 y2[1] (numeric) = 1.886626914449487 absolute error = 2.220446049250313e-16 relative error = 1.176939665306446e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 1.886626914449488 y1[1] (numeric) = 1.886626914449487 absolute error = 2.220446049250313e-16 relative error = 1.176939665306446e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4101 Order of pole (three term test) = 22.21 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4101 Order of pole (three term test) = 22.21 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.100000000000001 y2[1] (analytic) = 1.891207360061436 y2[1] (numeric) = 1.891207360061435 absolute error = 2.220446049250313e-16 relative error = 1.174089153913922e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 1.891207360061436 y1[1] (numeric) = 1.891207360061435 absolute error = 2.220446049250313e-16 relative error = 1.174089153913922e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.4042 Order of pole (three term test) = 22.21 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.4042 Order of pole (three term test) = 22.21 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.110000000000001 y2[1] (analytic) = 1.895698685680048 y2[1] (numeric) = 1.895698685680048 absolute error = 2.220446049250313e-16 relative error = 1.171307479412936e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 1.895698685680048 y1[1] (numeric) = 1.895698685680048 absolute error = 2.220446049250313e-16 relative error = 1.171307479412936e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3983 Order of pole (three term test) = 22.2 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3983 Order of pole (three term test) = 22.2 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.120000000000001 y2[1] (analytic) = 1.900100442176505 y2[1] (numeric) = 1.900100442176505 absolute error = 2.220446049250313e-16 relative error = 1.168594038485072e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 1.900100442176505 y1[1] (numeric) = 1.900100442176505 absolute error = 2.220446049250313e-16 relative error = 1.168594038485072e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3922 Order of pole (three term test) = 22.19 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3922 Order of pole (three term test) = 22.19 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.130000000000001 y2[1] (analytic) = 1.904412189378826 y2[1] (numeric) = 1.904412189378826 absolute error = 2.220446049250313e-16 relative error = 1.165948244625849e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 1.904412189378826 y1[1] (numeric) = 1.904412189378826 absolute error = 2.220446049250313e-16 relative error = 1.165948244625849e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3859 Order of pole (three term test) = 22.18 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3859 Order of pole (three term test) = 22.18 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.140000000000001 y2[1] (analytic) = 1.908633496115884 y2[1] (numeric) = 1.908633496115883 absolute error = 2.220446049250313e-16 relative error = 1.163369527868486e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 1.908633496115884 y1[1] (numeric) = 1.908633496115883 absolute error = 2.220446049250313e-16 relative error = 1.163369527868486e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3794 Order of pole (three term test) = 22.17 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3794 Order of pole (three term test) = 22.17 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.150000000000001 y2[1] (analytic) = 1.912763940260521 y2[1] (numeric) = 1.912763940260521 absolute error = 4.440892098500626e-16 relative error = 2.321714669033216e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 1.912763940260521 y1[1] (numeric) = 1.912763940260521 absolute error = 2.220446049250313e-16 relative error = 1.160857334516608e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3729 Order of pole (three term test) = 22.17 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3729 Order of pole (three term test) = 22.17 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.160000000000001 y2[1] (analytic) = 1.916803108771767 y2[1] (numeric) = 1.916803108771767 absolute error = 6.661338147750939e-16 relative error = 3.475233380657095e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 1.916803108771767 y1[1] (numeric) = 1.916803108771767 absolute error = 4.440892098500626e-16 relative error = 2.316822253771397e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3661 Order of pole (three term test) = 22.16 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3661 Order of pole (three term test) = 22.16 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.170000000000001 y2[1] (analytic) = 1.920750597736136 y2[1] (numeric) = 1.920750597736135 absolute error = 6.661338147750939e-16 relative error = 3.468091149159201e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 1.920750597736136 y1[1] (numeric) = 1.920750597736136 absolute error = 4.440892098500626e-16 relative error = 2.312060766106134e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3592 Order of pole (three term test) = 22.15 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3592 Order of pole (three term test) = 22.15 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.180000000000001 y2[1] (analytic) = 1.924606012408021 y2[1] (numeric) = 1.92460601240802 absolute error = 4.440892098500626e-16 relative error = 2.307429193232276e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 1.924606012408021 y1[1] (numeric) = 1.92460601240802 absolute error = 2.220446049250313e-16 relative error = 1.153714596616138e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3522 Order of pole (three term test) = 22.15 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3522 Order of pole (three term test) = 22.15 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.190000000000001 y2[1] (analytic) = 1.928368967249167 y2[1] (numeric) = 1.928368967249167 absolute error = 2.220446049250313e-16 relative error = 1.15146327645886e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 1.928368967249167 y1[1] (numeric) = 1.928368967249167 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.345 Order of pole (three term test) = 22.14 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.345 Order of pole (three term test) = 22.14 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.200000000000001 y2[1] (analytic) = 1.932039085967227 y2[1] (numeric) = 1.932039085967226 absolute error = 4.440892098500626e-16 relative error = 2.298551893052104e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 1.932039085967227 y1[1] (numeric) = 1.932039085967227 absolute error = 2.220446049250313e-16 relative error = 1.149275946526052e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3377 Order of pole (three term test) = 22.13 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3377 Order of pole (three term test) = 22.13 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.210000000000001 y2[1] (analytic) = 1.935616001553386 y2[1] (numeric) = 1.935616001553386 absolute error = 4.440892098500626e-16 relative error = 2.294304291211007e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 1.935616001553386 y1[1] (numeric) = 1.935616001553386 absolute error = 2.220446049250313e-16 relative error = 1.147152145605504e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3303 Order of pole (three term test) = 22.12 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3303 Order of pole (three term test) = 22.12 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.220000000000001 y2[1] (analytic) = 1.939099356319068 y2[1] (numeric) = 1.939099356319067 absolute error = 2.220446049250313e-16 relative error = 1.145091427117648e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 1.939099356319068 y1[1] (numeric) = 1.939099356319068 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3227 Order of pole (three term test) = 22.12 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3227 Order of pole (three term test) = 22.12 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.230000000000001 y2[1] (analytic) = 1.942488801931698 y2[1] (numeric) = 1.942488801931697 absolute error = 4.440892098500626e-16 relative error = 2.286186717825299e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 1.942488801931698 y1[1] (numeric) = 1.942488801931698 absolute error = 2.220446049250313e-16 relative error = 1.14309335891265e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.315 Order of pole (three term test) = 22.11 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.315 Order of pole (three term test) = 22.11 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.240000000000001 y2[1] (analytic) = 1.945783999449539 y2[1] (numeric) = 1.945783999449539 absolute error = 2.220446049250313e-16 relative error = 1.141157523074748e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 1.945783999449539 y1[1] (numeric) = 1.945783999449539 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.3072 Order of pole (three term test) = 22.11 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.3072 Order of pole (three term test) = 22.11 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.250000000000001 y2[1] (analytic) = 1.948984619355587 y2[1] (numeric) = 1.948984619355586 absolute error = 4.440892098500626e-16 relative error = 2.278567031467372e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 1.948984619355587 y1[1] (numeric) = 1.948984619355586 absolute error = 2.220446049250313e-16 relative error = 1.139283515733686e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2992 Order of pole (three term test) = 22.1 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2992 Order of pole (three term test) = 22.1 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.260000000000001 y2[1] (analytic) = 1.952090341590516 y2[1] (numeric) = 1.952090341590516 absolute error = 2.220446049250313e-16 relative error = 1.137470946883097e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 1.952090341590516 y1[1] (numeric) = 1.952090341590516 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2912 Order of pole (three term test) = 22.09 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2912 Order of pole (three term test) = 22.09 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.270000000000001 y2[1] (analytic) = 1.955100855584692 y2[1] (numeric) = 1.955100855584692 absolute error = 2.220446049250313e-16 relative error = 1.13571944020569e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 1.955100855584692 y1[1] (numeric) = 1.955100855584692 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.283 Order of pole (three term test) = 22.09 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.283 Order of pole (three term test) = 22.09 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.280000000000001 y2[1] (analytic) = 1.958015860289225 y2[1] (numeric) = 1.958015860289225 absolute error = 2.220446049250313e-16 relative error = 1.13402863290511e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 1.958015860289225 y1[1] (numeric) = 1.958015860289225 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2747 Order of pole (three term test) = 22.08 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2747 Order of pole (three term test) = 22.08 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.290000000000001 y2[1] (analytic) = 1.960835064206073 y2[1] (numeric) = 1.960835064206073 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 1.960835064206073 y1[1] (numeric) = 1.960835064206073 absolute error = 2.220446049250313e-16 relative error = 1.132398175544334e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2663 Order of pole (three term test) = 22.08 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2663 Order of pole (three term test) = 22.08 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.300000000000001 y2[1] (analytic) = 1.963558185417193 y2[1] (numeric) = 1.963558185417193 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 1.963558185417193 y1[1] (numeric) = 1.963558185417193 absolute error = 2.220446049250313e-16 relative error = 1.130827731890481e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2578 Order of pole (three term test) = 22.07 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2578 Order of pole (three term test) = 22.07 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.310000000000001 y2[1] (analytic) = 1.966184951612734 y2[1] (numeric) = 1.966184951612734 absolute error = 2.220446049250313e-16 relative error = 1.129316978765922e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 1.966184951612734 y1[1] (numeric) = 1.966184951612734 absolute error = 0 relative error = 0 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2491 Order of pole (three term test) = 22.07 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2491 Order of pole (three term test) = 22.07 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.320000000000001 y2[1] (analytic) = 1.968715100118265 y2[1] (numeric) = 1.968715100118265 absolute error = 2.220446049250313e-16 relative error = 1.12786560590556e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 1.968715100118265 y1[1] (numeric) = 1.968715100118266 absolute error = 2.220446049250313e-16 relative error = 1.12786560590556e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2404 Order of pole (three term test) = 22.06 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2404 Order of pole (three term test) = 22.06 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.330000000000001 y2[1] (analytic) = 1.971148377921045 y2[1] (numeric) = 1.971148377921045 absolute error = 2.220446049250313e-16 relative error = 1.126473315820192e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 1.971148377921045 y1[1] (numeric) = 1.971148377921045 absolute error = 2.220446049250313e-16 relative error = 1.126473315820192e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2316 Order of pole (three term test) = 22.06 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2316 Order of pole (three term test) = 22.06 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.340000000000001 y2[1] (analytic) = 1.97348454169532 y2[1] (numeric) = 1.973484541695319 absolute error = 4.440892098500626e-16 relative error = 2.25027964733166e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 1.97348454169532 y1[1] (numeric) = 1.97348454169532 absolute error = 2.220446049250313e-16 relative error = 1.12513982366583e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2227 Order of pole (three term test) = 22.05 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2227 Order of pole (three term test) = 22.05 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.350000000000001 y2[1] (analytic) = 1.975723357826659 y2[1] (numeric) = 1.975723357826659 absolute error = 4.440892098500626e-16 relative error = 2.247729714237781e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 1.975723357826659 y1[1] (numeric) = 1.97572335782666 absolute error = 4.440892098500626e-16 relative error = 2.247729714237781e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2137 Order of pole (three term test) = 22.05 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2137 Order of pole (three term test) = 22.05 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.360000000000001 y2[1] (analytic) = 1.977864602435316 y2[1] (numeric) = 1.977864602435316 absolute error = 4.440892098500626e-16 relative error = 2.245296312514325e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 1.977864602435316 y1[1] (numeric) = 1.977864602435317 absolute error = 4.440892098500626e-16 relative error = 2.245296312514325e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.2046 Order of pole (three term test) = 22.04 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.2046 Order of pole (three term test) = 22.04 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.370000000000001 y2[1] (analytic) = 1.979908061398614 y2[1] (numeric) = 1.979908061398614 absolute error = 4.440892098500626e-16 relative error = 2.242978946892899e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 1.979908061398614 y1[1] (numeric) = 1.979908061398615 absolute error = 4.440892098500626e-16 relative error = 2.242978946892899e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1954 Order of pole (three term test) = 22.04 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.1954 Order of pole (three term test) = 22.04 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.380000000000001 y2[1] (analytic) = 1.98185353037236 y2[1] (numeric) = 1.981853530372359 absolute error = 4.440892098500626e-16 relative error = 2.240777146465637e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 1.98185353037236 y1[1] (numeric) = 1.98185353037236 absolute error = 4.440892098500626e-16 relative error = 2.240777146465637e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1862 Order of pole (three term test) = 22.04 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.1862 Order of pole (three term test) = 22.04 NO COMPLEX POLE (six term test) for Equation 2 TOP MAIN SOLVE Loop x[1] = 1.390000000000001 y2[1] (analytic) = 1.983700814811277 y2[1] (numeric) = 1.983700814811276 absolute error = 4.440892098500626e-16 relative error = 2.238690464480713e-14 % Correct digits = 16 h = 0.01 y1[1] (analytic) = 1.983700814811277 y1[1] (numeric) = 1.983700814811277 absolute error = 4.440892098500626e-16 relative error = 2.238690464480713e-14 % Correct digits = 16 h = 0.01 NO INFO (given) for Equation 1 NO POLE (ratio test) for Equation 1 Radius of convergence (three term test) for eq 1 = 0.1769 Order of pole (three term test) = 22.03 NO COMPLEX POLE (six term test) for Equation 1 NO INFO (given) for Equation 2 NO POLE (ratio test) for Equation 2 Radius of convergence (three term test) for eq 2 = 0.1769 Order of pole (three term test) = 22.03 NO COMPLEX POLE (six term test) for Equation 2 Finished! diff ( y2 , x , 4 ) = y1 - 1.0 ; diff ( y1 , x , 1 ) = m1 * diff ( y2 , x , 3 ) ; Iterations = 130 Total Elapsed Time = 0.0 Seconds Elapsed Time(since restart) = 0.0 Seconds Time to Timeout = 10 Minutes 0.0 Seconds Percent Done = 100.8 %